Dependence of the Gleisberg Cycle Period on the Length of Wolf's Numbers Series

Abstract

The concept of "Gleisberg cycle" arose from the analysis of a small amount of data for a series of Wolf numbers (WSN), which are characterized by varying degrees of reliability and with the key role of cycles 5-7 of the Dalton minimum. Back in the thirties of the last century, when analyzing the first 16 cycles was done, Gleisberg noted the frequency of their maximums in seven to eight cycles, and later gave an updated value of the period - about 80 years. In the works done over the past 60 years, this period is evaluated within 80 - 110 years. A number of researchers allocate a specific value for the Gleisberg cycle period equals to 88 years. Since different authors analyzed a series of Wolf numbers of different lengths, it makes sense to investigate the influence of the length of the series itself on this period. The paper analyzes the long-period components of WSN versions v1 and v2. The connection between the period and the length of the series is found through the sine approximation of the corresponding fragments. An increase in the sine period from 82 to 110 years (for v1) was obtained with an increase in the length of the series from 18 to 24 cycles and the conditions for the local manifestation of the 88-year harmonic. The initial periodicity of the maximums of seven to eight cycles is transformed into ten to eleven cycles. The WSN series includes recovered data from 1749 to 1849 and further on, regular observation data - reliable data. The dependence of the period on the length of the series, that is, on the share of reliable data, is associated with the inconsistency of the characteristics of the reconstructed and reliable series and casts doubt on the existence of the Gleisberg cycle or “secular” harmonic in the WSN readings in the 1749-2015 interval. changes in the land cover by temporal analysis.